What is the limit as x approaches 0 of 1/x-1/(e^x) ?

The limit as x approaches 0 of 1/x-1/(e^x) is diverges

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limit as x approaches 0 of 1/x-1/(e^x)

x \to 0 lim (\frac{1}{x} - \frac{1}{e ^{x}})

diverges

Solution steps

x \to 0 lim (\frac{1}{x} - \frac{1}{e ^{x}})

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

x \to 0 + lim (\frac{1}{x} - \frac{1}{e ^{x}}) = \infty

x \to 0 - lim (\frac{1}{x} - \frac{1}{e ^{x}}) = - \infty

= diverges

What is the limit as x approaches 0 of 1/x-1/(e^x) ?
The limit as x approaches 0 of 1/x-1/(e^x) is diverges